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On a question ofMakar-Limanov

Author(s): Zinovy Reichstein
Journal: Proc. Amer. Math. Soc. 124 (1996), 17-19.
MSC (1991): Primary 16S10; Secondary 20M05
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Abstract: Let $K$ be an uncountable field, let $K \subset F$ be a field extension, and let $A$ be an associative $K$ -algebra. We show that if $F \otimes _K A$ contains a non-commutative free algebra, then so does $A$ .

References:

L1: L. Makar-Limanov, On free subsemigroups of skew fields, Proc. Amer. Math. Soc. 91 (1984), 189--191.MR 85j:16022
L2: ------, On free subobjects of skew fields, Methods in Ring Theory (F. van Oystaeyen, ed.), NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., vol. 233, Reidel, Dordrecht, 1984, pp. 281--285. CMP 17:06
LM: L. Makar-Limanov and P. Malcolmson, Free subalgebras of enveloping fields, Proc. Amer. Math. Soc. 111 (1991), 315--322. MR 91f:16023
K: A. A. Klein, Free subsemigroups of domains, Proc. Amer. Math. Soc. 116 (1992), 339--341.MR 92m:16045


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